## Linear Operators, Part 2 |

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Page 1019

Nelson Dunford, Jacob T. Schwartz. volume of any n - sided parallelepiped is

never larger than the volume of a rectangular parallelepiped with sides of the

same lengths . Proof . The

checked ...

Nelson Dunford, Jacob T. Schwartz. volume of any n - sided parallelepiped is

never larger than the volume of a rectangular parallelepiped with sides of the

same lengths . Proof . The

**inequality**is obvious for n = 1 and may be easilychecked ...

Page 1061

14 ) and Hölder ' s

. D . Having proved the basic

the full

14 ) and Hölder ' s

**inequality**, and the theorem is proved for all p , 1 < p < 0 . Q . E. D . Having proved the basic

**inequality**of M . Riesz , we now proceed to provethe full

**inequality**of Calderón and Zygmund . Our first step is to put the result of ...Page 1105

We now pause to sharpen another of the

continuity of the product TS which was noted in the paragraph following Lemma 9

, the continuity of the norm function which follows from the triangle

Lemma ...

We now pause to sharpen another of the

**inequalities**of Lemma 9 . ... thecontinuity of the product TS which was noted in the paragraph following Lemma 9

, the continuity of the norm function which follows from the triangle

**inequality**ofLemma ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function give given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero